Optimum detection of an optical image on a photoelectric surface.

The image-detecting performance of an optimum counting detector is compared with that of a threshold detector and that of a detector basing its decisions on the total number of photoelectrons from a finite area of the image. The illuminance of the image is assumed to have a Gaussian spatial distribution. The optimum detector works with the pristine datum (and not with the photoelectric response) which is the spatiotemporal electromagnetic field at the aperture of the observing optical instrument. It is shown that little is to be gained by using details of the illuminance distribution beyond the crude knowledge of its breadth as embodied in a simple counter of emitted photoelectrons. All three detectors exhibit accordingly about the same reliability.